A travel agent collected data from a group of past clients regarding what type of reservation they plan to make in the future and which package they plan to choose. The types of reservations offered at the agency are tours, cruises, and resorts, and the packages offered are either basic or deluxe.

Answer:

Step-by-step explanation:

\(\frac{3x-y}{4x+5y}=\frac{3}{5}\\\\\)

Cross multiply

5*(3x-y) = 3*(4x + 5y)

5*3x -5*y = 3*4x + 3*5y

15x - 5y = 12x + 15y

15x - 12x = 15y + 5y

     3x    =  20y

     3x = 4y * 5

\(\frac{3x}{4y} = 5\)

Step-by-step explanation:

Answer:

Minimum Unit Cost = $14,362

Step-by-step explanation:

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.6

b = -108

c = 19,222

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

-(-108)/2(0.6) = 108/1.2 = 90

Plugging this value into original function would give us the minimum (unit cost):

To compute 101^(4,800,000,023) mod 35 using the Chinese Remainder Theorem, we need to first decompose 35 into its prime factors: 35 = 5 × 7.

Next, we need to compute 101^(4,800,000,023) mod 5 and 101^(4,800,000,023) mod 7 separately.

To compute 101^(4,800,000,023) mod 5, we can use Fermat's Little Theorem, which states that if p is a prime number and a is a positive integer not divisible by p, then a^(p-1) ≡ 1 mod p. Since 5 is prime and 101 is not divisible by 5, we have 101^(4) ≡ 1 mod 5. Therefore, 101^(4,800,000,023) ≡ 101^(4 × 1,200,000,005 + 3) ≡ (101^4)^1,200,000,005 × 101^3 ≡ 1^1,200,000,005 × 101^3 ≡ 1 × 101^3 ≡ 1 mod 5.

To compute 101^(4,800,000,023) mod 7, we can use Euler's Totient Theorem, which states that if a and m are coprime positive integers, then a^φ(m) ≡ 1 mod m, where φ(m) is Euler's totient function. Since 7 is prime and φ(7) = 6, we have 101^6 ≡ 1 mod 7. Therefore, 101^(4,800,000,023) ≡ 101^(6 × 800,000,003 + 5) ≡ (101^6)^800,000,003 × 101^5 ≡ 1^800,000,003 × 101^5 ≡ 101^5 ≡ 4 mod 7.

Now we can use the Chinese Remainder Theorem to combine the results. Let x ≡ 1 mod 5 and x ≡ 4 mod 7. Then we can write x = 5k + 1 for some integer k. Substituting this into the second congruence, we get 5k + 1 ≡ 4 mod 7, or equivalently, k ≡ 6 mod 7. Therefore, x = 5k + 1 ≡ 5(6) + 1 ≡ 31 mod 35.

Hence, 101^(4,800,000,023) mod 35 = x = 31.

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Answer:

First we have to turn it into slope intercept form which is y = mx  + b.

we need to isolate y. To do this, we have to subtract 8x from both sides to get

-y = -8x - 24

-25 is the y intercept and -8 is the slope.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The predicted win for 17000 attendance is 98.5.

Option (B) is correct.

To find the predicted number of wins for a team

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers.

Given that:

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams.

Attendance = 17,000

The regression equation is

\(y=4.9x+15.2\)

where x represents the attendance (in thousands) and ŷ is the predicted number of wins.

The required predicted number of wins can be calculated as,

\(y=4.9x+15.2\\\\\\y=4.96*17+15.2\\\\y=98.5 wins\)

Therefore, the predicted win for 17000 attendance is 98.5.

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The radius of circle B is 8/9 units.

In the question, we are asked to find the radius of the circle with a center at B, given that the radius of a circle with a center at A is 1 unit, and circles with a center at B and C are congruent.

The radius of the circle with a center at D is twice that of A, making the radius of the circle with a center at D to be 2.

We assume the radius of circle B to be r units.

Now, we have AD = 1, AB = 1 + r, DE = x (assumed), AE = 1 + x, BE = r, and BD = 2 - r.

Thus, in triangle BDE, using the Pythagoras Theorem, we can write:

BD² = DE² + BE²,

or, (2 - r)² = x² + r²,

or, 4 + r² - 4r = x² + r²,

or, x² = 4 - 4r ... (i),

or, x² = 4(1 - r),

or, x = 2√(1 - r) ... (ii).

In triangle ABE, using the Pythagoras Theorem, we can write that:

AB² = AE² + BE²,

or, (1 + r)² = (1 + x)² + r²,

or, 1 + r² + 2r = 1 + x² + 2x + r²,

or, 2r = x² + 2x.

Substituting the values of x² and x from (i) and (ii), we get:

2r = (4 - 4r) + 2(2√(1 - r)),

or, r = 2 - 2r + 2√(1 - r),

or, 3r - 2 = 2√(1 - r),

or, 9r² + 4 - 12r = 4 - 4r,

or, 9r² - 8r = 0,

or, r(9r - 8) = 0.

Thus, either, r = 0, which is not possible,

or, 9r - 8 = 0, or, r = 8/9.

Thus, the radius of circle B is 8/9 units.

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The provided question is incomplete. For the complete question, refer to the attachment.

Answer:

A) ∠1

Step-by-step explanation:

They are corresponding angles meaning that they are congruent to each other.

The congruent angle of angle 5 is \(\angle1\)

When a transversal line cuts two parallel lines. the, corresponding and alternate angles are equal.

From given figure, It is observed that,

Corresponding angles are,

      \(\angle1 =\angle5,\angle3=\angle7\)

Thus, the congruent angle of angle 5 is \(\angle1\)

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Given:

Consider the expression is:

\(48+12\)

To find:

The expression that is equivalent to the given expression.

Solution:

We have,

\(48\div 12\)

It can be written as:

\(48\div 12=12\times 4+12\times 1\)

Taking out the GCF, we get

\(48\div 12=12(4+1)\)

Therefore, the correct option is B.

Answer:

b. 12 (4+1)

Step-by-step explanation:

hope this helps you {ribbit}

~tsu-chan :p

If the radius of the sphere is 3.5 inches , then the volume is 130.85 inches³  and the surface area is 153.86 inches²  .

In the question,

it is given that , the shape of the exercise ball is a sphere ,

the radius of the sphere is = 3.5 inches ,

the volume of sphere is gives as

Volume = (4/3)πr³

= (4/3)π(3.5)³              ....using π = 3.14

= 130.85 inches³

and Surface Area of the Sphere is = 4πr²

= 4π(3.5)²               ....using π = 3.14

= 153.86 inches²

Therefore , If the radius of the sphere is 3.5 inches , then the volume is 130.85 inches³  and the surface area is 153.86 inches²  .

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The percent of young men that are shorter than the mean height of young women is 2.5%.

A data set with a normal distribution has the majority of its values clustered in the middle of the range and the remaining values tapering off symmetrically toward either end.

A continuous probability distribution for a real-valued random variable is known as a "normal distribution" in statistics.

Based on the information, the percentage will be calculated thus:

Z = (69.3 - 64) / 2.7 = 1.9630

So P(Z>1.96)= 1-P(Z<1.96)

(check standard normal table)

= 1-0.975

= 0.025

= 2.5%

The percentage is 2.5%.

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The value of \(a_{4} = 91\)

We have to find value of \(a_{4}\).

A sequence is a collection of elements that are arranged according to a specific pattern.

Arithmetic sequence is a sequence where each consequtive term has a common constant difference.

Now,

Given that value of \(a_{1} = 4\)

\(a_{n} = 4a_{n-1} -1 - 4\)

Then to find value of \(a_{4}\), we can find a_{2} , a_{3} as;

\(a_{2} = 4(a_{1} ) - 1-4\\a_{2} = 4(3) - 1 - 4 = 11\)

\(a_{3} = -4(a_{2} ) - 1\\4(11) - 1 - 4 = 39\)

Hence, the value of \(a_{4}\) as;

\(a_{4} = 4(a_{3} ) - 1-4\\a_{4} = 4(-39) -1 -4\\a_{4} = 91\)

Therefore, The value of \(a_{4}\)= 91.

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Answer:

Step-by-step explanation:

To find the surface area of a cylinder, we need to add the area of the circular bases to the lateral area (the curved surface).

The diameter of the cylinder is 9 inches, so the radius (r) is half of that, or 4.5 inches.

The height of the cylinder (h) is given as 15 inches.

The area of each circular base is πr^2. Therefore, the area of both bases is 2πr^2.

The lateral area of the cylinder is given by the formula 2πrh.

Substituting the values we have:

Area of both bases = 2πr^2 = 2π(4.5)^2 = 2π(20.25) = 40.5π

Lateral area = 2πrh = 2π(4.5)(15) = 135π

Total surface area = area of both bases + lateral area = 40.5π + 135π = 175.5π

Approximating π to 3.14, we get:

Total surface area = 175.5π ≈ 175.5(3.14) ≈ 551.07

Therefore, the surface area of the cylinder is approximately 551.07 square inches.

Step-by-step explanation:

Need to find the other leg of the right triangle using pythagorean theorem

145^2 = 87^2 + x ^2

x= 116 u

SO the veg garden is a trapezoid  with bases 140 and (116+ 140 = 256) and height 87 units

area  =  height + (base 1 + base 2) /2 = 87 * ( 140 + 256) /2 = 17 226 units^2

Answer:

this answer is -1.8

Step-by-step explanation:

because you add and subtract all of them

Answer:

0.9

Step-by-step explanation:

Basic angle =

\(cos { }^{ - 1} ( \frac{4}{5} ) = 36.870 \: degrees \\ \)

Therefore,

\(theta = 180 + 36.870 = 216.87 \: degrees\)

Therefore,

\( \sin( \frac{theta}{2} ) = \sin(108.435 ) = 0.9\)

Based on given conditions,

\(a²b + 3 ab - (-5 a²b - 9 ab) \)

\(→a²b + 3 ab + 5 a²b + 9 ab\)

\(→(a²b + 5 a²b) + (3ab + 9 ab\)

Now collecting the coefficients and adding them,

\((1 + 5)a²b + (3 + 9)ab\)

\(→6 {a}^{2}b + 12ab\)

Hence, the 6a²b + 12ab should be added.

Answer:

True.

Step-by-step explanation:

When converting a mixed number into an improper number, multiply the denominator by the whole number and then add the numerator.

Answer:

True

Step-by-step explanation:

I answered something like this before it's true because When converting a mixed number into an improper number, multiply the denominator by the whole number and then add the numerator.  ty Math notes -_-

Answer:

I think segment bisector or midpoint

Step-by-step explanation:

This is because to bisect means to split it evenly into 2

to bisect a segment means to split it to 2 even parts with a midpoint

Answer:

x = 20°

Step-by-step explanation:

by angle sum property of triangle

30 + 130 + x = 180

x = 180 - 160

Answer:

The area of the parallelogram is 247 inches^2 to the nearest square inch

Step-by-step explanation:

This question asks us to calculate the area of a parallelogram given the sides and an acute angle.

Please check attachment for diagrammatic representation of the said parallelogram.

Mathematically, the area of the parallelogram can be calculated using the formula;

A = ab sin θ

where a and b refers to the length of the two sides and θ being the acute angle

Substituting these values, we have

A = 20 * 14 * sin 62

A = 280 sin 62 = 247.23 which is 247 inches^2 to the nearest square inch

Answer:

8/40 + 20/40 = 28/40

Step-by-step explanation:

It's about finding the common denominator for the fractions.

we can easily see that 40 is a common denominator for denominators 10 and 4. 20 would work too, but 40 is "instantly seen".

2/10 = (2*4) / (10*4) = 8/40

2/4 = (2*10) / (4*10) = 20/40

8/40 + 20/40 = (8+20) / 40 = 28/40

Similarity: two triangle are similar (they have the same shape but generally different size) if and only if the have the same angles.

In this case, we have that:

ΔTSU ≅ ΔUVW

because they have the same angles

We know this because:

Vertical angles: when two lines are crossed, the opposite angles formed are equal. These angles are called vertical angles.

Since TS and VW are parallel

Alternate interior angles: when two parallel lines are crossed by a transversal, there are couples of angles formed that are equal. Those are called alternate interior angles.

ΔTSU ≅ ΔUVW

by vertical angles and alternate interior angles

If G is the incenter of triangle ABC the values of the unknown sides are

a) GD = 12

b) BG = 13.42

c) FC = 35

d) BF = 6

Considering that G is the incenter of triangle ABC, we have that

Using the right triangle CDG and applying Pythagoras theorem given by  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

GC² = GD² + DC²

37² = GD² + 35²

GD² = 37² - 35²

GD² = 144

take square root of both sides

GD = √144

GD = 12

Using the right triangle BEG to solve for BG

BG² = EB² + GE²

BG² = 6² + 12²

BG² = 180

take square root of both sides

BG = √180

BG = 13.42

Using the right triangle CFG to solve for FC

GC² = GF² + FC²

rearranging the equation

FC² = GC² - GF²

FC² = 37² - 12²

FC² = 1225

take square root of both sides

FC = √1225

FC = 35

Using the right triangle BFG to solve for BF

BG² = GF² + BF²

rearranging the equation

BF² = BG² - GF²

BF² = 13.42² - 12²

BF² = 36.0964

take square root of both sides

BF = √36.0964

BF = 6

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Roy purchased whole pizzas for P 190.00 each. To determine the number of whole pizzas he bought, we can divide the total cost of the pizzas by the cost of each pizza. Therefore, the calculation P 950.00 / P 190.00 results in 5, indicating that Roy bought five whole pizzas.

Roy spent a total of P 1070 for pizza with 3 sets of additional toppings. Since each set of additional toppings costs P 40.00, then the total cost of the toppings is 3 x P 40.00 = P 120.00. Subtracting this from the total amount spent gives us P 950.00, which is the cost of the pizzas alone.

Since each whole pizza costs P 190.00, we can divide the cost of the pizzas by the cost of each pizza to find the number of whole pizzas Roy bought. Therefore, P 950.00 / P 190.00 = 5.

Thus, Roy bought 5 whole pizzas.

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Answer:

Step-by-step explanation:

Height h = 4.5 inches

Radius r = 3.4/2 = 1.7 inches

Area of base = πr² = 2.89π square inches

Volume of cylinder = πr²h = 2.89π4.5 = 13.0 cubic inches

Answer:

The answer is 40.8

Step-by-step explanation:

The volume of a cone equals the area of a circle multiplied by the height

\(v = \pi \times {r}^{2} \times h \\ = 3.14 \times 1.7 \times 1.7 \times 4.5 \\ = 40.8\)

The probability that a card drawn at random from an ordinary deck of 52 playing cards is: (a) An ace is 1/13. (b) A jack of hearts is 1/52. (c) A three of clubs or a six of diamonds is 1/26. (d) A heart is 1/4. (e) Any suit except hearts is 3/4. (f) A ten or a spade is 4/13. (g) Neither a four nor a club is 10/13.

We will find the probability of the given situations.

a) An aceThere are 4 aces in the deck.

Therefore, the probability of drawing an ace is given by

P(Ace) = 4/52 = 1/13

b) A jack of hearts

There is only one jack of hearts in the deck.

Therefore, the probability of drawing a jack of hearts is given by

P(Jack of hearts) = 1/52

c) A three of clubs or a six of diamonds

There is one three of clubs and one six of diamonds in the deck.

Therefore, the probability of drawing a three of clubs or a six of diamonds is given by

P(Three of clubs or six of diamonds) = 2/52 = 1/26

d) A heart

There are 13 hearts in the deck.

Therefore, the probability of drawing a heart is given by

P(Heart) = 13/52 = 1/4

e) Any suit except hearts

There are 39 cards that are not hearts in the deck.

Therefore, the probability of drawing any suit except hearts is given by

P(Any suit except hearts) = 39/52 = 3/4

f) A ten or a spade

There are 16 cards that are either tens or spades.

Therefore, the probability of drawing a ten or a spade is given by

P(Ten or spade) = 16/52 = 4/13

g) Neither a four nor a club

There are 12 cards that are either fours or clubs.

Therefore, the probability of drawing neither a four nor a club is given by

P(Neither four nor club) = 40/52 = 10/13

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Answer:

Variable

Step-by-step explanation:

If you can substitute a unknown variable with another expression that is equal, you can then solve for another variable, and with that equal expression, solve for the first variable.

Answer

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

We can make the number 1.00 as 100%. We have to figure out how many times 0.25 goes into 1.00. 0.25 goes into 1.00 4 times. Now, we can divide 100 by 4 to get 25%

Hope this Helps!!! :)

Let me know in the comments if the answer was perfect or if I should change anything!!!